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Introduction to MATLAB

Introduction to MATLAB. Zongqiang Liao Research Computing Group UNC-Chapel Hill. Course outline. Introduction Getting started Mathematical functions Matrix generation Matrix and array operations Reading and writing data files Basic plotting Basic programming. Introduction.

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Introduction to MATLAB

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  1. Introduction to MATLAB Zongqiang Liao Research Computing Group UNC-Chapel Hill

  2. Course outline • Introduction • Getting started • Mathematical functions • Matrix generation • Matrix and array operations • Reading and writing data files • Basic plotting • Basic programming

  3. Introduction

  4. Introduction • The name MATLAB stands for MATrix LABoratory • It is good at dealing with matrices • Vendor’s website: http//:www.mathworks.com • Advantages of MATLAB • Easiness of use • Powerful build-in routines and toolboxes • Good visualization of results • Disadvantage of MATLAB • Can be slow

  5. Getting started

  6. Getting started • MATLAB desktop • The Command Window • The Command History • The Workspace • The Current Directory • The Help Browser • The Start Button

  7. Getting started • Keeping track of your work session • diary command >> diary or >> diary FileName • Stop the recording >> diary off • Start the recording again >>diary on

  8. Getting started • Using MATLAB as a calculator >> 1+2*3 ans = 7 • You may assign the value to a output variable >> x=1+2*3 x= 7 • x can be used in the some calculation later >> 4*x ans = 28

  9. Getting started • Suppressing output • You can suppress the numerical output by putting a semicolon (;) at the end of the line >> t=-13; • We can place several statements on one line, separated by commas (,) or semicolons(;) >> t=-13; u=5*t, v=t^2+u u= -65 v= 104

  10. Getting started • Managing the workspace • The results of one problem may have an effect on the next one • Issue a clear command at the start of each new independent calculation >> clear or >> clear all

  11. Getting started • Miscellaneous commands • To clear the Command Window >> clc • To abort a MATLAB computation ctrl-C • To continue a line …

  12. Getting started • Getting help • Use help to request info on a specific function >> help sqrt • Use doc function to open the on-line version of the help menu >> doc plot • Use lookfor to find function by keywords >> lookfor functionkeyword

  13. Mathematical functions

  14. Mathematical functions • Lists of build-in mathematical functions • Elementary functions >> help elfun • Special functions >> help specfun • Such as sin(x), cos(x), tan(x), ex, ln(x)

  15. Mathematical functions • Example 1 Calculate z=e-asin(x)+10 for a=5, x=2, y=8 >> a=5; x=2; y=8; >> z=exp(-a)*sin(x)+10*sqrt(y) z= 28.2904

  16. Mathematical functions • Example 2 Calculate the roots of a equation ax2+bx+c=0, for a=2, b=1, and c=-4 >> a=2; b=1; c=-4; >> x1=(-b+sqrt(b^2-4*a*c))/(2*a) x1= 1.1861 >> x2=(-b-sqrt(b^2-4*a*c))/(2*a) x2= -1.1861

  17. Mathematical functions • Example 3 >> log(142) ans= 4.9558 >> log10(142) ans= 2.1523

  18. Mathematical functions • Example 4 Calculate sin( /4) >> sin(pi/4) ans = 0.7071 Calculate e10 >> exp(10) ans = 2.2026e+004

  19. Matrix generation

  20. Matrix generation • The name MATLAB is taken from ”MATrix LABoratory.” It is good at dealing with matrices. • Actually all variables in MATLAB are matrices. • Scalars are 1-by-1 matrices • vectors are N-by-1 (or 1-by-N) matrices. • You can see this by executing >> size(x)

  21. Matrix generation • Entering a matrix • Begin with a square bracket, [ • Separate elements in a row with spaces or commas (,) • Use a semicolon (;) to separate rows • End the matrix with another square bracket, ]

  22. Matrix generation • Entering a matrix: A typical example >> A=[1 2 3; 4 5 6; 7 8 9] >> A= 1 2 3 4 5 6 7 8 9

  23. Matrix generation • Matrix indexing • View a particular element in a matrix • For example, A(1,3) is an element of first row and third column >>A(1,3) >>ans = 3

  24. Matrix generation • Colon operator in a matrix • Colon operator is very useful in the usage of MATLAB • For example, A(m:n,k:l) specifies portions of a matrix A: rows m to n and column k to l.

  25. Matrix generation • Colon operator in a matrix • Example 1 Rows 2 and 3 and columns 2 and 3 of matrix A >>A(2:3, 2:3) ans = 5 6 8 9

  26. Matrix generation • Colon operator in a matrix • Example 2 Second row element of matrix A >>A(2, :) ans = 4 5 6

  27. Matrix generation • Colon operator in a matrix • Example 3 Last two columns of matrix A >>A(:, 2:3) ans = 2 3 5 6 8 9

  28. Matrix generation • Colon operator in a matrix • Example 4 Last rows of matrix A >>A(2:end, :) ans = 4 5 6 7 8 9 The end here denotes the last index in the specified dimension

  29. Matrix generation • Transposing a matrix • The transposing operation is a single quote (’) >>A’ ans = 1 4 7 2 5 8 3 6 9

  30. Matrix generation • Concatenating matrices • Matrices can be made up of sub-matrices >>B= [A 10*A; -A [1 0 0; 0 1 0; 0 0 1]] B = 1 2 3 10 20 30 4 5 6 40 50 60 7 8 9 70 80 90 -1 -2 -3 1 0 0 -4 -5 -6 0 1 0 -7 -8 -9 0 0 1

  31. Matrix generation • Generating vectors: colon operator • Suppose we want to enter a vector x consisting of points (0, 0.1, 0.2, 0.3,…,5) >>x=0:0.1:5; • All the elements in between 0 and 5 increase by one-tenth

  32. Matrix generation • Generating vectors: linear spacing • Suppose we want to have direct control over the number of points. >>y=linspace(a, b, n) For example, >>theta=linspace(0, 2*pi, 101) Creates a vector of 101 elements in the interval

  33. Matrix generation • Elementary matrix generators • eye(m,n) • eye(n) • zeros(m,n) • ones(m,n) • diag(A) • rand(m,n) • randn(m,n) • logspace(a,b,n) • For a complete list of elementary matrices >>help elmat >>doc elmat

  34. Matrix arithmetic operation

  35. Matrix arithmetic operation • Arithmetic operations • A+B or B+A • A*B • A^2 or A*A • a*A or A*a

  36. Matrix arithmetic operation • Matrix functions • det • diag • eig • inv • norm • rank

  37. Matrix arithmetic operation • Matrix functions • For example >> A=[1 2 3; 4 5 6; 7 8 0]; >>inv(A) ans = -1.7778 0.8889 -0.1111 1.5556 -0.7778 0.2222 -0.1111 0.2222 -0.1111 >>det(A) ans = 27

  38. Matrix arithmetic operation • More matrix operations • Calculate the sum of elements in the second row of matrix A >> sum(A(2,:)) • Calculates the sum of the last column of A >>sum(A(:,end))

  39. Array arithmetic operation

  40. Array arithmetic operation • Array operations • Array operations are done element-by-element • The period character (.) is used in array operations • The matrix and array operations are the same for addition (+) and subtraction (-)

  41. Array arithmetic operation • Array operations If A and B are two matrices of the same size with elements A=[aij] and B=[bij] • C=A.*B produces a matrix C of the same size with elements cij= aijbij • C=A./B produces a matrix C of the same size with elements cij= aij/bij • C=A.^2 produces a matrix C of the same size with elements cij= aij2

  42. Array arithmetic operation • Array operations • Example 1 A= B= >>C=A.*B C= 10 40 90 160 250 360 490 640 810

  43. Array arithmetic operation • Array operations • Example 2 >>C=A.^2 C= 1 4 9 16 25 36 49 64 81

  44. Reading and writing data files

  45. Reading and writing data files • Save and load data file • Use command save to save the variable in the workspace • For example, use command save: >> x = [1 3 -4]; >> y = [2 -1 7]; >> z = [3 2 3]; >> save Filename.mat The command saves all variables in the workspace into a binary file Filename.mat

  46. Reading and writing data files • Save and load data file • Save only certain variables by specifying the variable names after the file name >> save Filename.mat x y • Save variables into ASCII data file >> save Filename.dat x y –ascii

  47. Reading and writing data files • Save and load data file • The data can be read back with the load command >> load Filename.mat • Load only some of the variables into memory >> load Filename.mat x • Load the ASCII data file back into memory >> load Filename.dat -ascii

  48. Reading and writing data files • The textread function • The load command assumes all of data is of a single type • The textread function is more flexible, it is designed to read ASCII files where each column can be of a different type • The command is: >> [A,B,C,...] = textread(filename, format, n);

  49. Reading and writing data files • The textread function • For example, if a text file “mydata.dat” contains the following lines: tommy 32 male 78.8 sandy 3 female 88.2 alex 27 male 44.4 saul 11 male 99.6 • The command is: >> [name,age,gender,score] = textread(‘mydata.dat’, ‘%s %d %s %f’, 4);

  50. Reading and writing data files • C style read/write • MATLAB allows C style file access. It is crucially important that a correct data format is used. • The steps are: • Open a file for reading or writing. A unique file identifier is assigned. • Read the data to a vector • Close the file with file identifier

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